<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">C. Y. CHAN</style></author><author><style face="normal" font="default" size="100%">P. TRAGOONSIRISAK</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A QUENCHING PROBLEM DUE TO A CONCENTRATED NONLINEAR SOURCE IN AN INFINITE STRIP</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">35B35</style></keyword><keyword><style  face="normal" font="default" size="100%">35K55</style></keyword><keyword><style  face="normal" font="default" size="100%">35K57</style></keyword><keyword><style  face="normal" font="default" size="100%">35K60</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2011</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2011</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/20/33-DSA-31-20.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">20</style></volume><pages><style face="normal" font="default" size="100%">13</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;This article studies a semilinear parabolic initial-boundary value problem with a concentrated nonlinear source in an infinite strip in the N-dimensional Euclidean space. Existence, uniqueness, and locations where quenching occurs for the solution are investigated.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">505</style></section></record><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">C. Y. CHAN</style></author><author><style face="normal" font="default" size="100%">P. TRAGOONSIRISAK</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">EFFECTS OF A CONCENTRATED NONLINEAR SOURCE ON QUENCHING IN R N</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">35K57</style></keyword><keyword><style  face="normal" font="default" size="100%">35K60</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2009</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2009</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/18/04-DSA-CY-4-ChanTragoonsirisak.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">18</style></volume><pages><style face="normal" font="default" size="100%">7</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;. Let T and α be positive real numbers, β be a real number, B be a N-dimensional ball  x ∈ R N : |x| &amp;lt; R centered at the origin with a radius R, and ∂B be its boundary. Also, let ν(x) denote the unit inward normal at x ∈ ∂B, and χB(x) be the characteristic function, which is 1 for x ∈ B, and 0 for x ∈ R N \ B. This article studies the following parabolic Cauchy problem with a concentrated nonlinear source on ∂B: ut − 4u = α(1 + |x|) β ∂χB(x) ∂ν f(u) in R N × (0, T], u(x, 0) = 0 for x ∈ R N , u(x, t) → 0 as |x| → ∞ for 0 &amp;lt; t ≤ T, where f is a given function such that limu→c− f(u) = ∞ for some positive constant c, and f(u) and its derivatives f 0 (u) and f 00(u) are positive for 0 ≤ u &amp;lt; c. It is shown that the solution u always quenches for N ≤ 2, and quenching can be prevented for any β for N ≥ 3. For given R and β, the effects of α on quenching are discussed. Similarly for a given α, the effects of R and β on quenching are investigated.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">47</style></section></record></records></xml>